Andrei Shelankov

Charge transfer counting statistics revisited

Charge transfer statistics of quantum particles is obtained by analysing the time evolution of the many-body wave function. Exploiting properly chosen gauge transformations, we construct the probabilities for transfers of a discrete number of particles. Generally, the derived formula for counting statistics differs from the one previously obtained by Levitov et al. (J. Math. Phys., 37 (1996) 4845). The two formulae agree only if the initial state is prohibited from being a superposition of different charge states. Their difference is illustrated for cases of a single particle and a tunnel junction, and the role of charge coherence is demonstrated.

Quasiclassical theory of superconductivity: A multiple-interface geometry

This Thesis is concerned with the quasiclassical theory of meso-scopic superconductivity. The aim of the Thesis is to introduce the boundary conditions for a quasiclassical Green’s function on partially transparent interfaces in mesoscopic superconducting structures and to analyze the range of applicability of the quasiclassical theory. The linear boundary conditions for Andreev amplitudes, factoring the quasiclassical Green’s function, are presented. The quasiclassical theory on classical trajectories is reviewed and then generalized to include knots with paths intersections. The main focus of the Thesis is on the range of validity of the quasiclassical theory. This goal is achieved by comparison of quasiclassical and exact Green’s functions. The exact Gor’kov Greens function cannot be directly used for the comparison because of its strong microscopic variations on the length-scale of λF. It is the coarse-grain averaged exact Green’s function which is appropriate for the comparison. In most of the typical cases the calculations show very good agreement between both theories. Only for certain special situations, where the classical trajectory contains loops, one encounters discrepancies. The numerical and analytical analysis of the role of the loop-like structures and their influence on discrepancies between both exact and quasiclassical approaches is one of the main results of the Thesis. It is shown that the terms missing in the quasiclassical theory can be attributed to the loops formed by the interfering paths. In typical real samples any imperfection on the scale larger than the Fermi wavelength disconnects the loops and the path is transformed into the tree-like graph. It is concluded that the quasiclassical theory is fully applicable in most of real mesoscopic samples. In the situations where the conventional quasiclassical theory is inapplicable due to contribution of the interfering path, one can use the modification of the quasiclassical technique suggested in the Thesis.

Non-Abelian gauge fields in the gradient expansion: Generalized Boltzmann and Eilenberger equations

We present a microscopic derivation of the generalized Boltzmann and Eilenberger equations in the presence of non-Abelian gauges for the case of a nonrelativistic disordered Fermi gas. A unified and symmetric treatment of the charge

Quantum measurement in charge representation

[U(1)]

The Aharonov-Bohm wave and the Cornu spiral

and spin

Laser controlled magnetism in hydrogenated fullerene films

[SU(2)]

Noise spectrum of a tunnel junction coupled to a nanomechanical oscillator

degrees of freedom is achieved. Within this framework, just as the

Magnetic Properties of Polymerized Fullerene Doped with Hydrogen, Fluorine and Oxygen

U(1)

Squeezed states of a particle in magnetic field

Lorentz force generates the Hall effect, so does its

Bogoliubov-de Gennes versus quasiclassical description of Josephson layered structures

SU(2)